Runge-Kutta 4th Order Method
Simultaneous Ordinary
Differential Equations I
College of Engineering
Environmental Engineering Department
3th Stage
Mr. Waleed Ali Tameemi
M.Sc. Kansas University/USA
Outline
 Introduction
 Initial Value Problems

Runge-Kutta 4th Order Method
Euler’s Method
Improved Euler’s Method
Boundary Value Problems (Finite Differences Method)
Simultaneous Ordinary
Differential Equations
Two ordinary deferential equations
and
Initial condition
Required
(
and z value at a given x value
Step size
Number of steps
Methodology
Runge-Kutta 4th Order
Method
Runge-Kutta 4th Order
Method